In the following background and description a distinction is made between a resonator and an oscillator. A resonator is generally a piezoelectric device that vibrates mechanically when stimulated by an electric signal. An oscillator comprises a resonator and ancillary components to supply the stimulus signal to the resonator.
In the prior art, sustaining circuits for mechanical oscillators typically control the operation of the resonator in its linear operating range. The drive levels used in the prior art are significantly low in order to prevent nonlinear elastic behavior of the resonator to prevent various instabilities from developing. For quartz and other piezoelectric oscillators, several sustaining circuits are currently widely used such as Pierce, Colpitts, and Clapp designs. These circuits consist of simple amplifiers and passive capacitive elements for providing static gain and phase control around the loop for overcoming resistive losses in the resonator and maintaining a 2π positive feedback. An example of a Pierce circuit is shown in FIG. 1. The Pierce circuit can be implemented with an amplifier 140, a crystal 142, and two capacitors 144 and 146, to produce the output 150.
More sophisticated circuits have been developed for temperature compensation using a microprocessor and look-up tables for determining the voltages to be applied to varactors within the loop for frequency pulling, such as a microcomputer compensated crystal oscillator (MCXO) designs. Other automatic gain control circuits have been developed to prevent the gain of the amplifiers from saturating and thus introducing extraneous noise at the output.
Because all current piezoelectric-resonator-based oscillators operate in the linear elastic regime of the resonator, the sustaining circuits that are currently being utilized only have simple gain stages and gain limiters for the amplifier within the control loop. None of these circuits are designed to work and stabilize the operating point around nonlinear features of the admittance curves of the resonators. In addition, there has been a long-felt belief that the lowest phase noise is obtained when an oscillator/resonator is run in the linear regime, because in many circuits nonlinearities typically produce extraneous noise through intermodulation distortions, mixing, and uncontrollable behavior.
B. Yurke, et al. in Physical Review A. Vol 51#5, 1995, pp 4211-4224 describe that for an oscillator using a silicon beam resonator the output noise of an amplifier in sustaining circuitry for an oscillator can contribute to the overall frequency noise (phase noise) of the oscillator, and that this electronic noise component of the total phase noise of the oscillator can be minimized by setting the operating point near or at the critical point of the resonator. Yurke further teaches that at this critical point, the slope of the phase shift across the resonator as a function of frequency approaches infinity, and that this high phase slope reduces the contribution of phase noise from the electronics from producing frequency or phase noise in the oscillator output. Further that a critical point may be produced by driving the amplitude of the resonator to a high enough level to produce a cubic functionality of the elastic constant.
What is needed is a apparatus and method for improved phase noise reduction using nonlinear characteristics of piezoelectric resonators. The embodiments of the present disclosure answer these and other needs.